European Frequency and Time Seminar (EFTS) quartz tuning fork laboratory session.

A quartz tuning fork packaged in a transparent casing is used to demonstrate

• closed loop oscillation using a Negative Impedance Converter (NIC) circuit (Allan deviation below $10^{-9}$ up to 30 s integration time).
• openloop stroboscopic imaging of the quartz prong motion driven by sound card output.

KiCAD board design files.

References:

Hardware

• 32768 Hz tuning fork in transparent package: Epson FC-135 32.7680KA-AC5 (0.404 euros/p)
• sound card with sampling rate 96 kHz or higher, e.g. UGREEN (10.2 euros on amazon)
• "digital microscope" webcam, e.g. AmScope HHD Series (~50 euros)
• 7414 Schmitt trigger (0.5 to 0.7 euros)
• 7400 NAND gate (0.2 to 0.3 euros)

Software

• use mplayer tv:// to display the webcam output since vlc does not seem to display properly on the Raspberry Pi 5
• GNU Radio flowchart for driving the two channels of the stereo sound card (tested with GNU Radio 3.10) with 1 Hz offset between the signal driving the tuning fork and the stroboscopic signal driving the LED.

Resources:

Equivalent BvD model of the quartz tuning fork:

• R1=53727 $\Omega$
• L1=7221 H
• C1=3.268 fF
• C0=3.368 pF

Quality factor $Q=\frac{1}{R1}\sqrt{\frac{L1}{C1}}=27700$

Resonance frequency $f=\frac{1}{2\pi\sqrt{L1\cdot C1}}=\frac{1}{2\pi\sqrt{7221\times 3.268\cdot 10^{-15}}}=32763$ Hz